We study the effect of the antisymmetric tensor field B_{mu u} on the large curvature phase of string cosmology. It is well-known that a non-vanishing value of H=dB leads to an anisotropic expansion of the spatial dimensions. Correspondingly, in the string phase of the model, including α' corrections, we find anisotropic fixed points of the evolution, which act as regularizing attractors of the lowest order solutions. The attraction basin can also include isotropic initial conditions for the scale factors. We present explicit examples at order α' for different values of the number of spatial dimensions and for different ansätze for H.